>>> 2021-02-20 555 500 710 etc
We are probably all familiar with "555" telephone numbers. The basic idea is that the 555 exchange code (or NXX in a NANP NXX-XXXX number) is reserved for use in fiction. Of course, this isn't actually true at all, but that hasn't stopped basically every work of fiction putting their imaginary telephone numbers in the 555 exchange.
In reality, the 555 exchange has a somewhat bumpy history, as is the case with most "special purpose" telephone ranges. Seemingly from the genesis of NANP as a formal numbering standard, the 555 exchange was reserved for special use by telcos, and was not to be used for normal subscriber lines. The 555 exchange accumulated various and sundry uses, but most prominently, starting in the early '60s it was used for directory service at 555-1212 in nearly all NPAs (area codes). This was nearly the only successful use of the 555 exchange, leaving it mostly empty.
Because the 555 exchange was conveniently largely out of use, it became common for the entertainment industry to use 555 numbers in fiction. Wikipedia makes the claim that the telephone industry had specifically recommended 555 numbers for this use in the '60s, and while this is rather thinly sourced, it's not hard to believe as any odd person in a technical role at a telephone company might have suggested 555 as an exchange with extremely few assigned numbers.
In any case, the use of 555 numbers for fiction was somewhat informal. This changed in 1994, when the telephone industry regretted leaving an entire exchange out of use and formed a working group which allowed 555 numbers to be assigned to nationwide communications services. The idea was that 555 numbers would have the unusual property of working nationwide when dialed as only seven digits, somewhat like an early version of SMS short codes.
Because the use of 555 numbers in fiction was longstanding, the working group explicitly reserved numbers starting 555-01 for use in fiction. This, in 1994, is when this practice became formalized---but only for those 100 numbers.
In practice the 555 service as imagined was unsuccessful, and in the 2010s the use was eliminated more or less by handshake agreement. Much like the pre-1994 state, the only valid phone numbers in the 555 exchange are 555-1212 for directory assistance, and 555-4334. This latter number is apparently still assigned for a nationwide use but no one specifies what use.
I did a bit of digging, and... came up empty. 555-4334 in a number of area codes turns up nothing from the CNAM service I use. Similar attempts with a couple of validation/carrier lookup vendors returned different types of useless results. I haven't found any mention of the number in old newspapers, with the interesting exception of some newspapers listing their classified ads with exclusively 555 numbers, including 4334.
It was not an unusual practice at the time for newspapers to provide special "voice mail box" numbers for classified ads, but to my knowledge the use of 555 was not typical. The first newspapers to do so were almost all in Utah, which hints that it may have originated as a choice by a local telco, potentially Mountain Bell but maybe more likely an independent. I will do some more digging into this over time. It's interesting in that it suggests a major use of 555 numbers which no document I've seen on the history of the exchange mentions. This practice doesn't seem to have been eliminated until the 1994 reallocation.
I also learned that in 2009 you could get a rebate of $7,555 or $4,334 on a new Dodge Nitro. Isn't OCR fun?
Finally, I located an older FCC report (dated 1997) that lists 555-4334 as allocated to MCI mail, an early e-mail service. MCI mail access was initially by modem, and so it's possible that 555-4334 was used as an access number, although an 800 number was also provided for this purpose and 4334 is not mentioned anywhere I can find as an access number. An interesting feature of MCI Mail was its ability to forwarded email to postal addresses (by printing and mailing it) or by fax or teletype, so I speculate that 555-4334 may have been used as a return number for TTY messages, since the TTY integration was apparently bidirectional. In any case, another document noted that 555-4334 was permitted to remain in service until that service ended, which may have been an allowance due to the fact that MCI was a telephone carrier (and thus had greater sway over the working group) and that replacing the number may have been technically difficult.
Today, it remains the case that only 555-01xx is properly allocated for fictional use. However, the 555 exchange as a whole is as dead (or considering the use by newspapers, much more dead) than ever before, so it remains common to use the entire 555 exchange in fiction.
Oddly, the 555 NPA (rather than exchange) is allocated for similar applications, but as far as I can tell it is not in use.
The failure of the post-1994 use of 555 for a "short dialing service" reflects a larger series of telco failures that has left some other special prefixes. In the '90s, a great deal of attention was directed towards "non-geographic" dialing. Because the telephone system connected the nation together, why not have a method of telephone dialing which is independent of geography? Well, as it turns out, there are several reasons, but this didn't stop anyone from trying.
Although there were a hodgepodge of other attempts, the first major non-geographic dialing scheme is contained in the special 700 NPA (area code). This NPA was allocated as a direct result of the breakup of the Bell system for use directly by interexchange (long-distance) carriers, since all existing numbering ranges were allocated to the exchange (local) carriers. The primary service offered in this range was "EasyReach 700" from AT&T, which was basically carrier-managed "follow-me."
Follow-me is a common feature of business telephone systems that allows a call to a given number (extension or DID) to be directed to one or more real extensions depending on the location of the intended recipient. For example, a call to a professional might go to their desk or to an assistant depending on whether they are in the office, while an auto mechanic might have a call to a general contact number ring at the front desk or in the shop depending on where they are.
EasyReach 700 moved this same concept from the PABX to the telephone network, making it possible for follow-me to span the nation and making it accessible to businesses without an (expensive) PABX. For example, a consumer with two different homes could get a 700 number and set it to forward to whichever house they were staying in, while a traveling salesman could set their 700 number to forward to whichever hotel they were staying in.
EasyReach was a failure. There were several reasons, but the most significant relates to the billing climate of the time. Today, unlimited long-distance is so ubiquitous that the issue may not be obvious, or you might naively assume that AT&T had found a way to resolve the long distance cost issue. They did not---in fact, they came up with something worse. The owner of a 700 number could set it up to either bill forward (to the caller) or reverse (to the callee). This meant that the caller of a 700 number had virtually no way to determine whether the call would be free or charged at long-distance rate, and this was a huge deterrent to use of these numbers.
Today, this and other uses of the 700 NPA have all died out, leaving 700 a nearly empty NPA. Like other empty NPAs, 700 is sometimes hijacked for special uses by non-mainstream carriers and corporate phone systems. If my hazy memory is correct, the 700 NPA was used by GE's interoffice leased-line long distance network when I briefly worked for a GE business. Wikipedia says that WalMart still uses it this way.
Since the 700 NPA was such a success, AT&T naturally decided to do it again. In 1993, NANP allocated the 500 NPA to Personal Communications Service (PCS), not to be confused with Personal Communications Service (PCS). In fact, the same term was allocated to two completely different purposes by two different telecom organizations within a few years. The latter refers to a set of services offered by a wireless network, e.g. Sprint PCS, while the former refers to... EasyReach 700 all over again, except for now it's called True Connections.
True Connections failed for the exact same reasons as EasyReach 700, and was officially eliminated in 2000, but by this point AT&T had already largely replaced it with a service using 800 numbers which were of course always reverse billed... which you and I might think is obviously what they should have done in the first place, but back in the '90s toll-free and non-geographic were viewed as being different animals. It seems to have taken AT&T a long time to catch on to the fact that the realities of long-distance billing required that they be closely linked.
The concept of PCS (the non-geographic dialing one) did not die out with True Connections, and additional NPAs were allocated to the same purpose, generally in the format of 5 followed by the same digit twice, much like 800. 500 numbers continue to be non-geographic and the billing situation remains odd, but that hasn't stopped the use of 500 for certain uses like modem banks for ISPs and some calling cards. Very few 500 numbers remain in use today despite the multiple allocated 500 codes, and due to the billing issues it's common for outbound calls to 500 numbers to be blocked. Similar to 700, it's not unusual for 500 to be used for internal purposes, although this is probably less of a good idea since PCS services in the 500 NPA have not officially been ended.
500 and related PCS area codes (500 has a surprising number of overlays considering how obscure its usage is) also see use for other miscellaneous telco applications. For example, the 588 area code, also assigned to PCS, was (and may still be) used by Verizon Wireless to generate temporary phone numbers used to bridge their proprietary enhanced SMS service to other carriers.
The 500 NPA is sometimes referred to today as a "machine to machine" service, since it's now largely used for modems. Another set of NPAs reserved for machine-to-machine uses were a set ending in 10 - 510, 610, 710, 810, 910. These were used for an AT&T-run (later Western Union) teletext service, in which these numbers were used for higher-quality local circuits with TTYs attached. The service was successful in its era, but after the advent of the fax machine fell out of use.
In 1983, the now-unused 710 NPA was reallocated to the US Federal Government, making it de facto a non-geographic NPA. While the 710 area code had once been envisioned as a unifying NPA for federal offices throughout the country (this made a great deal of sense since most federal offices had their telephone service on special contract terms with AT&T that allowed for free calling between them), but this never seems to have caught on. As far as I can tell, for the entire history of 710's assignment to the federal government it has only contained one valid number, 710-627-4387, which is the access number for the Government Emergency Telephone Service (GETS). Telephone call prioritization schemes like this may be a topic I cover in the future. 710's "waste of space" has attracted some criticism.
The 600 area code, following a pattern, is also allocated for non-geographic use but in Canada, and has some overlay codes (611, 622, etc) as well. These numbers are apparently rare, being used for specialized machine-to-machine and arctic telephone services. Logically the 666 area code would be allocated for this use, but it has been skipped.
The 456 NPA was briefly assigned to carrier-specific use (similar to 500) but specifically for inbound international calls, but this never seems to have received use other than a service to identify the carrier in use for international calls. Nonetheless, it is mildly interesting that there once existed an NPA that was intended only for use by callers outside of the NANP area.
The 950 exchange code had also formerly had a special meaning to access competitive long-distance carriers, but this was replaced by the 101 "dial-around" codes often referred to as 10-10 numbers. 950 is still reserved as an exchange code today.
Are there any other special telephone prefixes? (besides these and of course 800 and 900, which I plan to and have discussed separately, respectively). One commonly cited example are "test exchanges," exchange prefixes (NXX) that contain only test numbers. I would call these "quasi-standard" in that they tended to be consistent between similar makes and models of telephone switches, so there are common patterns. For example, 222, 958, and 959 are commonly used as exchange codes for test numbers---but just as commonly are assigned to actual subscribers. Ultimately it depends on the switch and sometimes how it is configured. In rare cases, three-digit numbers work for this purpose.
So that's a whole lot about non-geographical numbering. It's interesting that, as a broad trend, non-geographical telephone numbering other than toll free has been consistently unpopular in the US. This stands in contrast to a number of countries where cellular phones are typically numbered in non-geographical prefixes, which makes more sense than our American convention of assigning cellular phones NPAs based on where you lived in 2007. It's just tradition.
 I found a newspaper column which criticized it specifically because 710 was the last remaining unused "real" NPA. By real, the author meant an NPA with a 0 or 1 in the middle. For reasons I am not completely clear on, when NPAs were first assigned by AT&T, the middle digit was 0 for all NPAs which originally covered an entire state (e.g. 505 New Mexico, 503 Oregon), and 1 for NPAs which covered only a portion of a state (e.g. 212 New York City and 315 upstate New York). This scheme was abandoned as of the first NPA splits, since having to renumber the area covered by the new NPA was unpopular enough without having to renumber the old NPA as well to turn it into a 1 middle digit. That said, for many years most new NPAs retained a 0 or 1 middle digit.
 This isn't actually a footnote to anything, I just wanted to say that the listing of all assigned 555 numbers includes a range assigned to "Craig 'Tax Freeze' Freis", who would later run for president. His platform was his middle name.